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Research Papers

Utilization of a Two-Beam Cantilever Array for Enhanced Atomic Force Microscopy Sensitivity

[+] Author and Article Information
Samuel Jackson

Department of Mechanical Engineering,
University of Canterbury,
Ilam 8041, Christchurch, New Zealand
e-mail: samuel.jackson@pg.canterbury.ac.nz

Stefanie Gutschmidt

Department of Mechanical Engineering,
University of Canterbury,
Ilam 8041, Christchurch, New Zealand

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 2, 2017; final manuscript received December 9, 2017; published online February 23, 2018. Assoc. Editor: John Judge.

J. Vib. Acoust 140(4), 041004 (Feb 23, 2018) (10 pages) Paper No: VIB-17-1188; doi: 10.1115/1.4038943 History: Received May 02, 2017; Revised December 09, 2017

An array of cantilevers offers an alternative approach to standard single beam measurement in the context of atomic force microscopy (AFM). In comparison to a single beam, a multi-degrees-of-freedom system offers a greater level of flexibility with regard to parameter selection and tuning. By utilizing changes in the system eigenmodes as a feedback signal, it is possible to enhance the sensitivity of AFM to changes in sample topography above what is achievable with standard single beam techniques. In this paper, we analyze a two-beam array operated in FM-AFM mode. The array consists of a single active cantilever that is excited with a 90 deg phase-shifted signal and interacts with the sample surface. The active beam is mechanically coupled to a passive beam, which acts to vary the response between synchronized and unsynchronized behavior. We use a recently developed mathematical model of the coupled cantilever array subjected to nonlinear tip forces to simulate the response of the described system with different levels of coupling. We show that the sensitivity of the frequency feedback signal can be increased significantly in comparison to the frequency feedback from a single beam. This is a novel application for an AFM array that is not present in the literature.

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References

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Figures

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Fig. 1

Depiction of the macro scale array test rig used to analyze the coupled dynamics of an array of cantilevers. Each cantilever is 160 mm long, 40 mm wide, and 1.5 mm thick.

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Fig. 2

Physical representation of the two-beam array structure

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Fig. 3

Simulated frequency approach curves for a two beam array (red) and a single beam (blue) (a) Frequency approach curves with changing coupling. The solid red line represents an array with 9.5 mm of shared base material, which is close to the boundary of bifurcation in the approach curve. The dashed line represents an array with 9 mm of shared base material and the dotted line represents an array with 10 mm of shared base material. (b) Frequency approach curves with changing excitation amplitude. The solid red line represents an array with an excitation coefficient AĈ1=0.02. The dashed red line represents an array with an excitation coefficient AĈ1=0.02.

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Fig. 4

Simulated mode shapes of a two-beam array during FM-AFM operation in normalized units of displacement. A mode shape of 1 and 1 represents perfectly in-phase response and a mode shape of 1 and −1 represents perfectly out-of-phase response. The solid line represents an array with 9.5 mm of shared base material, the dashed line represents an array with 9 mm of shared base material and the dotted line represents an array with 10 mm of shared base material. The inserts are a visual representation of the mode shapes at the points represented by the vertical lines. Blue–Beam 1, Red–Beam 2.

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Fig. 6

Instantaneous frequency measured at the active cantilever while the system is held at the set point. The blue data points represent the single beam and the red data points represent the two beam array in the vicinity of frequency cross-over.

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Fig. 5

Instantaneous control input to the magnet actuator (control input is actuator velocity in units of mm s−1) while the system is held at the set point. The blue data points represent the single beam and the red data points represent the two beam array in the vicinity of frequency cross-over.

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